401k tax advantage vs lower fees in taxable account

Question

Is there a formula or rule of thumb to help determine when it's better to put money in a 401k, 403b etc. or a regular taxable account assuming similar investments and returns (for example the same index)? Match is not an issue.

I was thinking there could be some formula to plug in difference in fees, tax bracket today vs at retirement, and years remaining before retirement. Output would be estimated advantage of tax deferral.

I'm looking for more of a calculator or a formula than general rules of thumb. I already understand the general guidelines: tax deferral is better when fees are reasonable, you're in a high tax bracket now and expect to be in a lower one later, etc. But what I'm really looking for is a sense for how much the advantage is of tax deferral, quantitatively.

This is the closest I could come up with on my own:

• y = # years to retirement
• P = initial investment
• R = rate of return on underlying index/investment
• F = fee in 401k
• f = fee in taxable fund
• t/s = federal marginal tax rate now
• T/S = state marginal tax rate at retirement
• C = long-term capital gains tax rate (23.8% post-Obamacare, plus state)

Using 401k/tax deferral you end up with

[P*(1+R-F)^y] * (1-T-S)

With a taxable account you end up with

[P*(1-t-s)] * (1+R-f)^y * (1-C)

Does this remotely sound right?

Answer 1

Start with the tax delta. For example, you'd hope to deposit at 25% bracket, but take withdrawals while at a marginal 15%. In this case, you're 10% to the good with the 401(k) and need to look at the fee eating away at this over time. Pay an extra 1%/yr and after 10 years, you're losing money.

That's too simple, however. Along the way, you need to consider that the capital gain rate is lower than ordinary income. It's easier to take those gains as you wish to time them, where the 401(k) offers no flexibly for this. Even with low fees, this account is going to turn long term gains to ordinary income. (Note - in 2013, a couple with up to $72,500 in taxable income has a 0% long term cap gain rate. So, if they wish, they can sell and buy back a fund, claim the gain, and raise their cost basis. A tiny effort for the avoidance of tax on the gains each year.)

First paragraph, don't forget, there are the standard deduction, exemption, and 10% bracket. While you are in the range to save enough to create he income to fill the low end at withdrawal, there's more value than just the 10% I discussed earlier.

Last, there's a phenomenon I call The Phantom Tax Rate Zone when one's retirement withdrawals trigger the taxation of Social Security. It further complicates the math and analysis you seek.